Novel algorithm of large-scale simultaneous linear equations

2010 ◽  
Vol 22 (7) ◽  
pp. 074206
Author(s):  
T Fujiwara ◽  
T Hoshi ◽  
S Yamamoto ◽  
T Sogabe ◽  
S-L Zhang
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Simultaneous Linear Equations ◽  
Novel Algorithm

scholarly journals Random Number Generator Untuk Bobot Metode Conjugate Gradient Neural Network

2019 ◽  
Vol 4 (1) ◽  
pp. 19-25
Author(s):  
Yudistira Arya Sapoetra ◽  
Azwar Riza Habibi ◽  
Lukman Hakim
Keyword(s):  
Neural Network ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Random Number ◽  
Linear Equations ◽  
Random Number Generator ◽  
Random Weighting ◽  
Simultaneous Linear Equations ◽  
Speed Up ◽  
The Will

This research develops the theory of NN (neural network) by using CG (conjugate gradient) to speed up the process of convergence on a network of NN. CG algorithm is an iterative algorithm to solve simultaneous linear equations on a large scale and it is used to optimize the process of the network on backpropagation. In the process, a Neural netwok doing random weighting on the weight of v and w  and this weight will have an effect on the speed of convergence of an algorithm for NN by the method of CG. Furthermore, generating the random numbers to take a sample as a generator in this research of neural network by using uniform distribution (0,1) methods. Therefore, the aims of this research are to improve the convergence on NN weighting using numbers which are generated randomly by the generator and the will be corrected with the CG method.Keywords: neural network, backpropagation, weighting, conjugate gradient

An efficient approach to the seismogram synthesis for a basin structure using propagation invariants

1996 ◽  
Vol 86 (2) ◽  
pp. 379-388 ◽  
Author(s):  
H. Takenaka ◽  
M. Ohori ◽  
K. Koketsu ◽  
B. L. N. Kennett
Keyword(s):  
Integral Equation ◽  
Inverse Fourier Transform ◽  
Linear Equations ◽  
Computation Time ◽  
Reduction Technique ◽  
Final Solution ◽  
Space Domain ◽  
New Approach ◽  
Simultaneous Linear Equations ◽  
Single Integral

Abstract The Aki-Larner method is one of the cheapest methods for synthetic seismograms in irregularly layered media. In this article, we propose a new approach for a two-dimensional SH problem, solved originally by Aki and Larner (1970). This new approach is not only based on the Rayleigh ansatz used in the original Aki-Larner method but also uses further information on wave fields, i.e., the propagation invariants. We reduce two coupled integral equations formulated in the original Aki-Larner method to a single integral equation. Applying the trapezoidal rule for numerical integration and collocation matching, this integral equation is discretized to yield a set of simultaneous linear equations. Throughout the derivation of these linear equations, we do not assume the periodicity of the interface, unlike the original Aki-Larner method. But the final solution in the space domain implicitly includes it due to use of the same discretization of the horizontal wavenumber as the discrete wavenumber technique for the inverse Fourier transform from the wavenumber domain to the space domain. The scheme presented in this article is more efficient than the original Aki-Larner method. The computation time and memory required for our scheme are nearly half and one-fourth of those for the original Aki-Larner method. We demonstrate that the band-reduction technique, approximation by considering only coupling between nearby wavenumbers, can accelerate the efficiency of our scheme, although it may degrade the accuracy.

scholarly journals New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations

2020 ◽  
Vol 9 (5) ◽  
pp. 545-550
Keyword(s):  
Cloud Computing ◽  
Distributed Computing ◽  
Data Storage ◽  
Large Scale ◽  
Homomorphic Encryption ◽  
Linear Equations ◽  
Force Transmission ◽  
Large Scale Systems ◽  
Secure Outsourcing ◽  
Systems Of Linear Equations

Cloud computing is the on-request accessibility of computer system resources, specially data storage and computing power, without direct dynamic management by the client. In the simplest terms, cloud computing means storing and accessing data and programs over the Internet instead of your computer’s hard drive. Along the improvement of cloud computing, more and more applications are migrated into the cloud. A significant element of distributed computing is pay-more only as costs arise. Distributed computing gives strong computational capacity to the general public at diminished cost that empowers clients with least computational assets to redistribute their huge calculation outstanding burdens to the cloud, and monetarily appreciate the monstrous computational force, transmission capacity, stockpiling, and even reasonable programming that can be partaken in a compensation for each utilization way Tremendous bit of leeway is the essential objective that forestalls the wide scope of registering model for clients when their secret information are expended during the figuring procedure. Critical thinking is a system to arrive at the pragmatic objective of specific instruments that tackles the issues as well as shield from pernicious practices.. In this paper, we examine secure outsourcing for large-scale systems of linear equations, which are the most popular problems in various engineering disciplines. Linear programming is an operation research technique formulates private data by the customer for LP problem as a set of matrices and vectors, to develop a set of efficient privacypreserving problem transformation techniques, which allow customers to transform original LP problem into some arbitrary one while protecting sensitive input/output information. Identify that LP problem solving in Cloud component is efficient extra cost on cloud server. In this paper we are utilizing Homomorphic encryption system to increase the performance and time efficiency

scholarly journals A method of accelerating stationary iterative methods for solving linear systems

1988 ◽  
Vol 30 (1) ◽  
pp. 1-23
Author(s):  
G. K. Robinson
Keyword(s):  
Quadratic Forms ◽  
Simple Technique ◽  
Linear Equations ◽  
Full Rank ◽  
Systems Of Equations ◽  
Linear Combinations ◽  
Simultaneous Linear Equations ◽  
Large Systems ◽  
Stationary Iterative Methods ◽  
Refined Version

AbstractThe speed of convergence of stationary iterative techniques for solving simultaneous linear equations may be increased by using a method similar to conjugate gradients but which does not require the stationary iterative technique to be symmetrisable. The method of refinement is to find linear combinations of iterates from a stationary technique which minimise a quadratic form. This basic method may be used in several ways to construct refined versions of the simple technique. In particular, quadratic forms of much less than full rank may be used. It is suggested that the method is likely to be competitive with other techniques when the number of linear equations is very large and little is known about the properties of the system of equations. A refined version of the Gauss-Seidel technique was found to converge satisfactorily for two large systems of equations arising in the estimation of genetic merit of dairy cattle.

scholarly journals Alternating Asymmetric Iterative Algorithm Based on Domain Decomposition for 3D Poisson Problem

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 281
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Domain Decomposition ◽  
Iterative Algorithm ◽  
Poisson Equation ◽  
Large Scale ◽  
Linear Equations ◽  
Iterative Algorithms ◽  
Computation Time ◽  
Explicit Method ◽  
Computational Process ◽  
Poisson Problem

Poisson equation is a widely used partial differential equation. It is very important to study its numerical solution. Based on the strategy of domain decomposition, the alternating asymmetric iterative algorithm for 3D Poisson equation is provided. The solution domain is divided into several sub-domains, and eight asymmetric iterative schemes with the relaxation factor for 3D Poisson equation are constructed. When the numbers of iteration are odd or even, the computational process of the presented iterative algorithm are proposed respectively. In the calculation of the inner interfaces, the group explicit method is used, which makes the algorithm to be performed fast and in parallel, and avoids the difficulty of solving large-scale linear equations. Furthermore, the convergence of the algorithm is analyzed theoretically. Finally, by comparing with the numerical experimental results of Jacobi and Gauss Seidel iterative algorithms, it is shown that the alternating asymmetric iterative algorithm based on domain decomposition has shorter computation time, fewer iteration numbers and good parallelism.

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